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What is the original price of a commodity when the price elasticity is .71 and demand changes from 10 units to 15 units and the new price is?
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What is the original price of a commodity when the price elasticity is...
Understanding Price Elasticity of Demand
Price elasticity of demand measures how much the quantity demanded of a good responds to a change in price. In this scenario, the price elasticity is 0.71, indicating inelastic demand, meaning that demand changes less proportionately than the price does.
Calculating the Change in Demand
- Initial Demand: 10 units
- New Demand: 15 units
- Change in Demand: 15 - 10 = 5 units
Calculating the Percentage Change in Demand
- Percentage Change in Demand: (Change in Demand / Initial Demand) * 100
- Percentage Change: (5 / 10) * 100 = 50%
Using Price Elasticity to Find Price Change
Since we have the price elasticity of demand (PED) formula:
- PED = (% Change in Quantity Demanded) / (% Change in Price)
- Rearranging gives us: % Change in Price = (% Change in Quantity Demanded) / PED
Substituting the values:
- % Change in Price = 50% / 0.71 ≈ 70.42%
Calculating the Original Price
Let the original price be P. If the new price is P_new:
- P_new = P * (1 + % Change in Price)
- P_new = P * (1 + 0.7042) = P * 1.7042
Given that the new price is P_new, we can express the original price as:
- P = P_new / 1.7042
To find the original price, you need to know the new price. If, for example, the new price is $100:
- Original Price = $100 / 1.7042 ≈ $58.74
In conclusion, with the new price known, you can easily calculate the original price of the commodity.
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What is the original price of a commodity when the price elasticity is .71 and demand changes from 10 units to 15 units and the new price is?
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